Announcements - SOFIs, colloquium Friday at 2p in Newton 203, PRISM picnic Friday at 4p at Highland Park (Geneseo), and Senior Dinner Monday at 6p.  Don't forget papers due Monday and final exam a week from Tuesday in Milne 105 (bring computers).  

There are many great comments as we approach the end here.  I'm not posting many of them because I'm trying to use the time to discuss our final mathematical content, but I do greatly appreciate them.

Quick Answers 11.3

Blanch and the math. tables project were basically just a distributed human computing machine.  An interesting idea in context.  They computed improved tables and worked pretty efficiently because they could divide the work among a large number of people.  They also completed other computations on request.  Blanch's experience with business helped her know how to manage these people most efficiently.  

In Poland they said it was relatively inexpensive to support mathematicians.  Relative to what?  Probably scientists.  Remember we don't need big expensive labs.  Definitely then and sometimes still now, paper, pencil and wastebasket will do. 

Transfinite numbers are the heart of the study of modern set theory.  They are not numbers like other numbers you know, they are sizes of different infinite sets.  

The idea of an international journal wasn't radical, what was radical was "an international journal specifically devoted to a single field".  To have something so focused was a drastic change then.   It is very common now.  

In Vinogradov's argument that every sufficiently large odd number is the sum of three primes, says that there is some point after which it is sure to work.  I did some research and found:  Vinogradov's original "sufficiently large" N ≥ 3^(3^15} ~ 3.25x 10^6,846,168.  Wow!  That's big.  Thanks for asking, as I wouldn't have looked for this otherwise. 

Yes, the cardinality of the power set of of any set is equal to 2^|S|.

NEP is defined in the first paragraph in 11.3.4

"do history books that get taught in secondary and post secondary schools include some mathematics that occurred throughout history?  Every history textbook I remember, I do not recall any mathematics being discussed."  No, mostly because history teachers generally don't know much mathematics.  OTOH, in many cases math teachers don't know much history - I hope we've changed some of that.  

"Is Frederick Winslow Taylor the same mathematician to give us the Taylor series?"  Definitely not.  That was Brook Taylor around the time of Newton.  

Past:

We've said before that logic is a curious thing as to whether it's a part of mathematics - is it the method or the objects that define the field?  Today it is universally included.

Transcendental - not a solution to any polynomial equation.